I’m having trouble figuring out this simple math problem. I have spent over two hours reading through various related answers on SO and Google, but it seems my high school math knowledge is gone.

On the page I have an element, that, once it passes a threshold, gets scaled down, the closer it gets to the edge of the containing element. Right now, it scales in a linear fashion. I calculate the distance to the container’s edge, compare it to the **threshold value** (where the scale is 100%) and calculate a **percentage** from that, that is used to actually scale the Element (via CSS transform).

What I would like, is for the scaling to start slowly for about the first 60-80% and then ramp up considerably.

To me it seems I need some sort of inverse exponential or logarithmic function to do this, but I can’t figure out exactly how to implement this. Ideally, the function would return `0.0`

for `x = threshold`

and `1.0`

for `x = 0`

(where x would be the element’s current position/percentage).

Any help is appreciated. I think this is probably trivial, but I cannot wrap my head around it.

## Answer

Here’s two you could try:

(cos(pi*x) + 1) / 2

1 - x^2

Depending on if you want them to ease out or be steep at the threshold. These are normalized to (0,1), but you can easily scale them to whatever interval by dividing x by your threshold.